Encyclopedia of Systems and Control

2015 Edition
| Editors: John Baillieul, Tariq Samad

Bounds on Estimation

  • Arye Nehorai
  • Gongguo Tang
Reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5058-9_69


We review several universal lower bounds on statistical estimation, including deterministic bounds on unbiased estimators such as Cramér-Rao bound and Barankin-type bound, as well as Bayesian bounds such as Ziv-Zakai bound. We present explicit forms of these bounds, illustrate their usage for parameter estimation in Gaussian additive noise, and compare their tightness.


Barankin-type bound Cramér-Rao bound Mean-squared error Statistical estimation Ziv-Zakai bound 
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This work was supported in part by NSF Grants CCF-1014908 and CCF-0963742, ONR Grant N000141310050, AFOSR Grant FA9550-11-1-0210.


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Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • Arye Nehorai
    • 1
  • Gongguo Tang
    • 2
  1. 1.Preston M. Green Department of Electrical and Systems EngineeringWashington University in St. LouisSt. LouisUSA
  2. 2.Department of Electrical Engineering & Computer ScienceColorado School of MinesGoldenUSA